Adaptive equalization filter and method for updating filter coefficients

ABSTRACT

An aspect of the present invention is an adaptive equalization filter for an optical transmission system, including: a main signal filter; and a coefficient computation unit that updates the filter coefficient of the main signal filter. The pre-stage filter and the post-stage filter receive a sample of the main signal as an input. The pre-stage coefficient computation unit obtains the filter coefficient of the pre-stage filter by feedback control using the gradient method. The post-stage coefficient computation unit obtains the filter coefficient of the post-stage filter by feedforward control. The convolution computation unit obtains the filter coefficient of the main signal filter by convolution computation of the filter coefficient of the pre-stage filter obtained by the pre-stage coefficient computation unit and the filter coefficient of the post-stage filter obtained by the post-stage coefficient computation unit.

TECHNICAL FIELD

The present invention relates to technique of an adaptive equalizationfilter and a filter coefficient update method.

BACKGROUND ART

In digital coherent transmission, equalization processing is performedusing digital signal processing (DSP) in order to compensate forwaveform distortion generated in an optical fiber. In the equalizationprocessing, an adaptive equalization filter is used to follow a dynamicchange in waveform distortion. The filter coefficient thereof isgenerally controlled using the gradient method. Non Patent Literature 1and Non Patent Literature 2 describe control of the filter coefficientusing the gradient method.

For controlling the filter coefficient, it is required to follow thefluctuation of the polarization state due to the fluctuation of theoptical fiber transmission line at high speed. As the polarizationfluctuation resistance, for example, resistance to fluctuation such as a50 kH term is required. It has also been reported that higher-speedpolarization fluctuation occurs due to a lightning strike.

In a conventional transmission method, a method of transmitting a signalhaving a high symbol rate on a single carrier has been the mainstream.In a conventional transmission method, since the symbol rate is high, asufficiently high following speed can be realized even by adaptivefilter control using the gradient method. However, in recent years,there has been a report that it is effective to reduce the symbol rateof modulation from the viewpoint of minimizing non-linear degradation inoptical fiber transmission. Therefore, a configuration in which aplurality of subcarriers is multiplexed at the stage of digital signalprocessing has attracted attention.

CITATION LIST Non Patent Literature

-   Non Patent Literature 1: K. Kikuchi, “Fundamentals of Coherent    Optical Fiber Communications,” J. Lightwave Tech., Vol. 34, No.    1, p. 157, 2016.-   Non Patent Literature 2: D. N. Godard, “Self-recovering equalization    and carrier tracking in two-dimensional data communication systems,”    IEEE Trans. Comm., Vol. 28, No. 11, 1980.

SUMMARY OF INVENTION Technical Problem

Two trends of lowering the modulation symbol rate of opticaltransmission and the need for high polarization fluctuation resistancepose challenges. That is, lowering the symbol rate such as subcarrierdivision transmission generally decreases the polarization fluctuationresistance. The adaptive equalization filter coefficient is updatedusing the gradient method, and the filter coefficient is updated using aknown symbol and a data symbol at that time. Therefore, when the symbolrate decreases, the symbol arrival time interval increases, and thus,there is a problem that the fluctuation following speed decreases.

In view of the above circumstances, an object of the present inventionis to provide technique capable of achieving both a high following speedand a high distortion compensation resistance even when the symbol ratedecreases.

Solution to Problem

An aspect of the present invention is an adaptive equalization filterfor an optical transmission system, including: a main signal filter; anda coefficient computation unit that updates a filter coefficient of themain signal filter, in which the coefficient computation unit includes:a pre-stage filter and a post-stage filter that are connected incascade, each having a sample of a main signal as an input; a pre-stagecoefficient computation unit that obtains a filter coefficient of thepre-stage filter by feedback control using a gradient method; apost-stage coefficient computation unit that obtains a filtercoefficient of the post-stage filter by feedforward control; and aconvolution computation unit that obtains a filter coefficient of themain signal filter by convolution computation of the filter coefficientof the pre-stage filter obtained by the pre-stage coefficientcomputation unit and the filter coefficient of the post-stage filterobtained by the post-stage coefficient computation unit.

An aspect of the present invention is a filter coefficient update methodfor updating a filter coefficient of a main signal filter, in which apre-stage filter and a post-stage filter are connected in cascade, eachhaving a sample of a main signal as an input, a pre-stage coefficientcomputation unit obtains a filter coefficient of the pre-stage filter byfeedback control using a gradient method, a post-stage coefficientcomputation unit obtains a filter coefficient of the post-stage filterby feedforward control, and a convolution computation unit obtains afilter coefficient of the main signal filter by convolution computationof the filter coefficient of the pre-stage filter obtained by thepre-stage coefficient computation unit and the filter coefficient of thepost-stage filter obtained by the post-stage coefficient computationunit.

Advantageous Effects of Invention

According to the present invention, it is possible to achieve both ahigh following speed and a high distortion compensation resistance evenwhen the symbol rate decreases.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a block diagram illustrating a configuration example of anadaptive equalization FIR filter according to an embodiment of thepresent invention.

DESCRIPTION OF EMBODIMENTS

An embodiment of the present invention will be described in detail withreference to the drawing.

FIG. 1 is a block diagram illustrating a configuration example of anadaptive equalization FIR filter according to the present embodiment. Anadaptive equalization FIR filter 1 can be used as a part of an opticalsignal reception device or an optical signal relay device for an opticaltransmission system. The adaptive equalization FIR filter 1 executes afilter coefficient update method described below. As illustrated in theFIGURE, the adaptive equalization FIR filter 1 includes FIR filters 11,12, 13, and 14, adders 31 and 33, and a coefficient computation unit 80.

The FIR filters 11, 12, 13, and 14 are filters each provided on a mainsignal path. The FIR filters 11, 12, 13, and 14 are also referred to as“main signal filters”. A main signal path includes a single-stage 2×2FIR filter. The filter coefficients of the FIR filters 11, 12, 13, and14 are dynamically updated by the coefficient computation unit 80.X-polarized input signals are inputted to the FIR filters 11 and 13.Y-polarized input signals are inputted to the FIR filters 12 and 14. TheFIR filters 11, 12, 13, and 14 act on the input signals on the basis ofrespective filter coefficients. Outputs from the FIR filters 11 and 12are passed to the adder 31. Outputs from the FIR filters 13 and 14 arepassed to the adder 33.

Each of the adder 31 and the adder 33 adds inputted signals and outputsthe result. The adder 31 adds the signals from the FIR filters 11 and 12and outputs the result as an X-polarized signal. The adder 33 adds thesignals from the FIR filters 13 and 14 and outputs the result as aY-polarized signal.

The coefficient computation unit 80 controls the FIR filters 11, 12, 13,and 14 provided on the main signal path. Specifically, the coefficientcomputation unit 80 acquires a sample of an input signal to the adaptiveequalization FIR filter 1. The coefficient computation unit 80calculates and updates the coefficients of the FIR filters 11, 12, 13,and 14 on the basis of the sample. The coefficient computation unit 80is configured to perform feedforward control on a partial tapcoefficient in order to increase the following speed of the adaptiveequalization FIR filter 1.

The coefficient computation unit 80 includes a pre-stage 2×2 FIR filter41, a post-stage 2×2 FIR filter 42, a pre-stage FIR coefficientcomputation unit 51, a post-stage FIR coefficient computation unit 52, aCPR phase estimation unit 61, and a convolution computation unit 71.

The pre-stage 2×2 FIR filter 41 and the post-stage 2×2 FIR filter 42 aretwo-stage 2×2 filters connected in cascade. Each of the pre-stage 2×2FIR filter 41 and the post-stage 2×2 FIR filter 42 is a two-inputtwo-output FIR filter. Note that a sample of a main signal is inputtedto the sequence of the pre-stage 2×2 FIR filter 41 and the post-stage2×2 FIR filter 42 connected in cascade. Note that a part of the inputtedmain signal is a known signal (known symbol). The coefficientcomputation unit 80 computes the filter coefficients of the pre-stage2×2 FIR filter 41 and the post-stage 2×2 FIR filter 42 using the knownsymbol. The pre-stage 2×2 FIR filter 41 is also simply referred to as a“pre-stage filter”. Moreover, the post-stage 2×2 FIR filter 42 is alsosimply referred to as a “post-stage filter”.

The pre-stage FIR coefficient computation unit 51 obtains thecoefficient of the pre-stage 2×2 FIR filter 41 using the steepestdescent method (gradient method), and performs feedback control on thepre-stage 2×2 FIR filter 41. Note that the pre-stage FIR coefficientcomputation unit 51 is also simply referred to as a “pre-stagecoefficient computation unit”.

Specifically, the pre-stage FIR coefficient computation unit 51 obtainsthe filter coefficient of the pre-stage 2×2 FIR filter 42 using thegradient method in a manner such that the error between the outputsignal from the post-stage 2×2 FIR filter 41 and the known signaldecreases.

More specifically, the pre-stage FIR coefficient computation unit 51computes a complex error between the result of performing frequencyoffset compensation and carrier phase compensation on an output signalfrom the post-stage 2×2 FIR filter 42 and the known symbol at the sametime position. Moreover, the pre-stage FIR coefficient computation unit51 calculates an inner product of an input sample to the pre-stage 2×2FIR filter 41 used to obtain an output signal from the post-stage 2×2FIR filter 42 and the coefficient of the post-stage 2×2 FIR filter 42,further applies frequency offset compensation and carrier phasecompensation, and obtains an update vector on the basis of a product ofa complex conjugate of the application result and the complex error.More specifically, for example, the pre-stage FIR coefficientcomputation unit 51 calculates an inner product of input samples to thepre-stage 2×2 FIR filter 41, which are used to obtain the output signalfrom the post-stage 2×2 FIR filter 42 and the number of which is thesame as the length of the post-stage 2×2 FIR filter 42 for one symbol ofthe output signal, and the coefficient of the post-stage 2×2 FIR filter42, further applies the frequency offset compensation and the carrierphase compensation, and multiplies the product of a complex conjugate ofthe application result and the complex error by a step size to obtain anupdate vector. The pre-stage FIR coefficient computation unit 51computes and updates the filter coefficient of the pre-stage 2×2 FIRfilter 41 using the update vector.

The post-stage FIR coefficient computation unit 52 obtains thecoefficient of the post-stage 2×2 FIR filter 42 using the minimum meansquare error method (MMSE) or the like, and controls the post-stage 2×2FIR filter 42. In other words, the post-stage FIR coefficientcomputation unit 52 controls the post-stage 2×2 FIR filter 42 with thefeedforward configuration. Note that the post-stage FIR coefficientcomputation unit 52 is also simply referred to as a “post-stagecoefficient computation unit”.

Specifically, the post-stage FIR coefficient computation unit 52 obtainsan inverse matrix of a covariance matrix of an input signal vector tothe post-stage 2×2 FIR filter 42 using a plurality of sets of an inputsignal vector to the post-stage 2×2 FIR filter 42 and the known signalsymbol at the time position obtained by applying the post-stage 2×2 FIRfilter 42 to the input signal vector. The post-stage FIR coefficientcomputation unit 52 obtains a correlation vector between the knownsignal symbol and an input signal vector to the post-stage 2×2 FIRfilter 42. Then, the post-stage FIR coefficient computation unit 52applies the inverse matrix of the covariance matrix to the correlationvector, and obtains the filter coefficient of the post-stage 2×2 FIRfilter 42 using the minimum mean square error method.

The post-stage FIR coefficient computation unit 52 may obtain the filtercoefficient of the post-stage 2×2 FIR filter 42 with the followingprocessing. That is, one of the coefficients of the length M taps of thetwo inputs of the post-stage 2×2 FIR filter 42 are denoted by hx[1],hx[2], . . . , and hx[M], and the other of the coefficients are denotedby hy[1], hy[2], . . . , and hy[M].

Then, the post-stage FIR coefficient computation unit 52 selects one ora plurality of tap time positions m among the above M taps, and performsthe following processing on each of the selected m. The post-stage FIRcoefficient computation unit 52 computes a provisional value y[m] of anoutput symbol of the post-stage FIR filter (42) by applying a filtercoefficient at a tap time position other than the tap time position m toan input signal vector to the post-stage FIR filter (42). Moreover, thepost-stage FIR coefficient computation unit 52 calculates a complexerror between the complex value of the known signal symbol correspondingto the time position of the provisional value y[m] and the complex valueof the provisional value y[m]. Moreover, the post-stage FIR coefficientcomputation unit 52 performs the following processing using one or aplurality of sets of the above complex error and an input signal vectorto the post-stage 2×2 FIR filter 42 used to compute the provisionalvalue y[m]. That is, the post-stage FIR coefficient computation unit 52obtains an inverse matrix of the 2×2 covariance matrix of the inputsignal vector to the post-stage 2×2 FIR filter 42, obtains a correlationvector between the complex error and the input signal vector to thepost-stage 2×2 FIR filter 42, and applies the inverse matrix of the 2×2covariance matrix to the correlation vector to calculate hx[m] andhy[m], which are the m-th tap coefficients. Through the aboveprocessing, the post-stage FIR coefficient computation unit 52 obtainsthe filter coefficient of the post-stage 2×2 FIR filter 42.

Note that the post-stage FIR coefficient computation unit 52 may performcomputation of multiplying each known signal by the complex conjugate ofthe phase rotation amount predicted from the estimated frequency offsetamount. As a result, the error of the filter coefficient to be obtainedcan be reduced.

The post-stage FIR coefficient computation unit 52 may further performcomputation of multiplying a symbol for which the carrier phasecompensation amount has already been estimated by a complex conjugate ofthe carrier phase compensation amount for each of the known signals.Moreover, the post-stage FIR coefficient computation unit 52 may furtherperform computation of multiplying a symbol for which the carrier phasecompensation amount has not been estimated yet by a complex conjugate ofthe representative value of the phase compensation amount of a symbolfor which the carrier phase compensation amount has already beenestimated.

The CPR phase estimation unit 61 estimates the carrier phasecompensation amount.

The convolution computation unit 71 performs convolution computation ofthe coefficient of the pre-stage 2×2 FIR filter 41 obtained by thepre-stage FIR coefficient computation unit 51 and the coefficient of thepost-stage 2×2 FIR filter 42 obtained by the post-stage FIR coefficientcomputation unit 52. A result of the convolution computation by theconvolution computation unit 71 is used as coefficients of the FIRfilters 11, 12, 13, and 14 of the main signal path. That is, theconvolution computation unit 71 updates the coefficients of the FIRfilters 11, 12, 13, and 14 using the above computation result.

Hereinafter, update processing of the tap coefficient of the main signalFIR filter will be described. A main parameter that determines theconfiguration of the circuit is first defined as follows. The mainsignal filter length is denoted by N_FIR. The tap length of thepost-stage filter (post-stage 2×2 FIR filter 42) is denoted by N_PST.The filter length of the pre-stage filter (pre-stage 2×2 FIR filter 41)is denoted by N_PRE. N_PRE=N_FIR−N_PST+1 is satisfied. The averaginglength of the tap coefficient calculation of the post-stage filter(post-stage 2×2 FIR filter 42) is denoted by N_PST_AVG.

The coefficient computation unit 80 computes a coefficient for updatingthe coefficient of the main signal filter using the known signal symbol.

That is, the coefficient computation unit 80 extracts continuous sampleshaving the length N_FIR with a sample corresponding to the time positionof the known symbol as the center, from samples of the signal inputtedto the coefficient computation unit 80. The coefficient computation unit80 updates the filter coefficient of the pre-stage 2×2 FIR filter 41 andupdates the filter coefficient of the post-stage 2×2 FIR filter 42 usingthe extracted samples having the length N_FIR and the reference value ofthe known signal. The coefficient computation unit 80 calculates thefilter coefficient of the main signal data by convolution computation ofthe filter coefficient of the pre-stage 2×2 FIR filter 41 and the filtercoefficient of the post-stage 2×2 FIR filter 42. Moreover, thecoefficient computation unit 80 also performs FOC compensation amountestimation and CPR compensation amount estimation. Note that FOC means“frequency offset compensation”. Moreover, CPR means “carrier phaserecovery”. CPR is also referred to as “carrier phase regeneration”.

The coefficient computation unit 80 repeatedly calculates the processingdescribed below for each known symbol. The coefficient computation unit80 may perform the calculation using all known symbols, or may selectonly necessary known symbols to use for the calculation.

The coefficient computation unit 80 extracts X-polarized and Y-polarizedinput data corresponding to the length N_FIR samples with a samplecorresponding to the time position of the known symbol as the center,from input samples to the adaptive equalization FIR filter 1. Vectors ofthe input data extracted here having the length N_FIR are defined asfir_in_x_ps and fir_in_y_ps, respectively.

Next, the coefficient computation unit 80 computes the output of thepre-stage 2×2 FIR filter 42 for the N_PST samples necessary for thepost-stage 2×2 FIR filter 41. The coefficient computation unit 80extracts the first sample to the N_PRE-th sample respectively from theinput data vectors fir_in_x_ps and fir_in_y_ps having the length N_FIRdefined above, and generates a vector having the length N_PRE. TheX-polarized vector and the Y-polarized vector are defined as xin andyin, respectively.

The four tap coefficients of the pre-stage 2×2 FIR filter 41 are denotedby pre_hxx, pre_hxy, pre_hyx, and pre_hyy. The X-polarized output valueof the pre-stage 2×2 FIR filter 41 is obtained as the sum of the innerproduct of the vector xin and the coefficient pre_hxx, and the innerproduct of the vector yin and the coefficient pre_hxy. Similarly, theY-polarized output of the pre-stage 2×2 FIR filter 41 is obtained as thesum of the inner product of the vector xin and the coefficient pre_hyx,and the inner product of the vector yin and the coefficient pre_hyy. Theoutput value of the pre-stage 2×2 FIR filter 41 will be described as ascalar.

Next, the coefficient computation unit 80 performs similar processing onthe second to the (N_PRE+1)-th xin and yin extracted respectively forvectors fir_in_x_ps and fir_in_y_ps, which are samples of input data tothe pre-stage 2×2 FIR filter 41. As described above, the coefficientcomputation unit 80 repeats the processing N_PST times while advancingthe position, thereby obtaining N_PST sample values to be inputs to thepost-stage 2×2 FIR filter 42.

Moreover, the coefficient computation unit 80 acquires a reference valueof a known symbol corresponding to the post-stage FIR output symbol. Forexample, assuming that amplitude values of the X-polarized in-phasecomponent (Inphase) and quadrature component (Qudarature) of the knownsymbol at a certain time are denoted respectively by ps_ref_xi andps_ref_xq, the complex signal is psx_ref=ps_ref_xi+jxps_ref_xq. Here, jis an imaginary unit. Similarly, when amplitude values of the in-phasecomponent and the quadrature component for the Y polarization of theknown symbol at a certain time are denoted respectively by ps_ref_yi andps_ref_yq, the complex signal is psy_ref=ps_ref_yi+j×ps_ref_yq.

The coefficient computation unit 80 stores the input vectors having theabove length N_PST samples to the post-stage 2×2 FIR filter 42 in abuffer together with the known symbol reference values correspondingthereto. In order to update the coefficients of the post-stage 2×2 FIRfilter 42, a plurality of known symbols is used. When a predeterminednumber of sets of the input vector to the post-stage 2×2 FIR filter 42and the known symbol reference value enough for normally computing thecoefficient are stored, the post-stage FIR coefficient computation unit52 executes computation for obtaining the coefficient of the post-stage2×2 FIR filter 42. The post-stage FIR coefficient computation unit 52can use again the set of the input value to the post-stage 2×2 FIRfilter 42 and the known symbol reference value already used to calculatethe coefficient of the post-stage 2×2 FIR filter 42.

The following description will describe a method in which the post-stageFIR coefficient computation unit 52 obtains the coefficient using onlyN_PST_AVG sets of the input value to the post-stage 2×2 FIR filter 42and the known symbol reference value that are stored. As describedabove, N_PST_AVG is the averaging length of the tap coefficientcalculation of the post-stage 2×2 FIR filter 42.

First, the coefficient computation unit 80 obtains the phase rotationamount for one symbol as the frequency offset compensation amount on thebasis of the estimated FOC compensation amount. The coefficientcomputation unit 80 denotes a vector obtained by giving the obtainedphase rotation amount for one symbol over the length of N_PST_AVGsymbols as a phase difference between preceding and following symbols byfoc_phi_vec. The post-stage FIR coefficient computation unit 52 maycompensate for the phase rotation amount with a phase angle or as acomplex value.

If there is a compensation amount in the time region already estimatedby CPR (carrier phase recovery) that can be used in coefficient updateof the post-stage 2×2 FIR filter 42, the coefficient computation unit 80uses the compensation amount also as a phase compensation amount of aCPR estimation value to be described later.

Here, the symbol region used for coefficient update of the post-stage2×2 FIR filter 42 also includes a symbol region for which the phaseestimation processing for the subsequently-placed CPR (carrier phaserecovery) has not been completed. In these symbol regions, the CPRcompensation amount is not obtained. For these symbol regions, the phasecompensation amount of the representative value is duplicated and used.The phase compensation amount of the representative value is, forexample, a phase compensation amount of the last symbol of a region forwhich the CPR compensation amount has already been obtained.

That is, the post-stage FIR coefficient computation unit 52 may furtherperform computation of multiplying each of the known signals by thecomplex conjugate of the carrier phase compensation amount for thesymbol for which the carrier phase compensation amount has already beenestimated. Moreover, the post-stage FIR coefficient computation unit 52may further perform computation of multiplying a symbol for which thecarrier phase compensation amount has not been estimated yet by acomplex conjugate of the representative value of the phase compensationamount of a symbol for which the carrier phase compensation amount hasalready been estimated.

The post-stage FIR coefficient computation unit 52 obtains the CPR phasecompensation amount cpr_phi_vec of the length N_PST_AVG symbol asdescribed above.

Next, the post-stage FIR coefficient computation unit 52 obtains a tapcoefficient of the post-stage 2×2 FIR filter 42. As a method therefor, aplurality of methods will be described below.

[First Method]

A first method is a method of collectively obtaining all taps of thepost-stage 2×2 FIR filter 42 using the minimum mean square error method.

An X-polarized input sample necessary for obtaining the output of onesymbol from the post-stage 2×2 FIR filter 42 can be expressed as a rowvector having the length N_PST. N_PST_AVG known symbols are used toupdate the coefficient of the post-stage 2×2 FIR filter 42. A matrixhaving N_PST_AVG rows in the vertical direction and N_PST columns in thehorizontal direction in which row vectors of N_PST_AVG samples of theX-polarized input signal to the post-stage 2×2 FIR filter 42corresponding to the time positions of the known symbols are arranged inthe vertical direction is denoted by PST_xall. Similarly, on the Ypolarization side of N_PST_AVG known symbols, a matrix having N_PST_AVGrows in the vertical direction and N_PST columns in the horizontaldirection in which row vectors of N_PST_AVG samples of input signals tothe post-stage 2×2 FIR filter 42 are arranged in the vertical directionis denoted by PST_yall. The two matrices PST_xall and PST_yall arecoupled in the horizontal direction to obtain a matrix having N_PST_AVGrows in the vertical direction and 2×N_PST columns in the horizontaldirection. This matrix is denoted by a X-polarized and Y polarized inputsample matrix PST_xyall. The post-stage FIR coefficient computation unit52 calculates a covariance matrix from the rectangular matrix PST_xyall.Specifically, the post-stage FIR coefficient computation unit 52computes a matrix product of the phase conjugate transposed matrix ofthe matrix PST_xyall and the matrix PST_xyall, and further divides thematrix product by N_PST_AVG to obtain a covariance matrix. Thecovariance matrix calculated in this manner is a square matrix having avertical size and a horizontal size of 2×N_PST.

Moreover, the post-stage FIR coefficient computation unit 52 arrangesN_PST_AVG known symbols to be used for coefficient update of thepost-stage 2×2 FIR filter 42 in the vertical direction to obtain a knownsymbol column vector ref (N_PST_AVG rows in the vertical direction andone column in the horizontal direction). The post-stage FIR coefficientcomputation unit 52 applies a complex conjugate transposed matrix of theX-polarized and Y-polarized input sample matrix PST_xyall to the aboveknown symbol column vector ref, and further divides the result byN_PST_AVG to obtain a correlation vector cor_xy.

Note that there is a problem here that an error in the coefficientcomputation increases due to occurrence of phase rotation for eachsymbol in a case where there is a frequency offset. In order to solvethis problem, the post-stage FIR coefficient computation unit 52 canreduce the error in the coefficient computation by multiplying eachcomponent of the above known symbol column vector ref by the complexconjugate of the frequency offset phase compensation vector foc_phi_vec.

Moreover, in a case where the phase noise is large, the post-stage FIRcoefficient computation unit 52 similarly can reduce the error of thecoefficient by multiplying each component of the known symbol columnvector ref by the complex conjugate of the CPR phase compensation amountvector cpr_phi_vec. That is, the post-stage FIR coefficient computationunit 52 may perform computation of multiplying each known signal by thecomplex conjugate of the phase rotation amount predicted from theestimated frequency offset amount.

In a case where the frequency offset compensation or the phase noisecompensation are performed, the post-stage FIR coefficient computationunit 52 applies the complex conjugate transposed matrix of theX-polarized and Y-polarized input sample matrix PST_xyall to the knownsymbol column vector ref, and further divides the result by N_PST_AVG toobtain the correlation vector cor_xy.

The post-stage FIR coefficient computation unit 52 can obtain the tapcoefficient of the post-stage 2×2 FIR filter 42 by computing the inversematrix of the covariance matrix for the correlation vector cor_xyobtained above. The tap coefficient obtained here has a length of2×N_PST, and is obtained by coupling hxx and hxy.

[Second Method]

Next, a second method for obtaining the tap coefficient of thepost-stage 2×2 FIR filter 42 will be described. In the second method,the coefficient of the post-stage 2×2 FIR filter 42 is simply computedusing inverse matrix computation of a 2×2 matrix (matrix having two rowsin the vertical direction and two columns in the horizontal direction)in order to avoid a mounting load for computing an inverse matrix of amatrix having three or more dimensions. The tap coefficients having thelength N_PST of the post-stage 2×2 FIR filter 42 are denoted by hxx[m],hxy[m], hyx[m], and hyy[m]. Here, m is an integer of 1 or more, andN_PST or less.

Similarly to the case of the first method, the input sample to thepost-stage 2×2 FIR filter 42 can be expressed as a row vector having thelength N_PST. A matrix having N_PST_AVG rows in the vertical directionand N_PST columns in the horizontal direction in which N_PST_AVG vectorsof X-polarized input samples are arranged in the vertical direction isdenoted by PST_xall. Similarly for the Y polarization side, a matrixhaving N_PST_AVG rows in vertical direction and N_PST columns in thehorizontal direction in which N_PST_AVG input samples that are rowvectors having the length N_PST are arranged in the vertical directionis denoted by PST_yall.

Known symbols corresponding to the output symbols outputted from thepost-stage 2×2 FIR filter 42 on the basis of the above input samples arearranged in the vertical direction to obtain a known symbol columnvector ref (N_PST_AVG rows in the vertical direction and one column inthe horizontal direction).

The post-stage FIR coefficient computation unit 52 first obtains tapcoefficients hxx[m] and hxy[m] corresponding to the number of taps ofthe X-polarized output. A selected m-th tap coefficient in the lengthN_PST of the coefficient is represented as hxx[m] and hxy[m]. The m isan integer of 1 or more, and N_PST or less. All other tap coefficientsare initial values or latest values that have been obtained at thattime. The initial value may be, for example, zero. Alternatively, avalue after the previous coefficient update may be used as the initialvalue. The post-stage FIR coefficient computation unit 52 performsfilter computation using an initial value as a filter coefficient otherthan the selected m-th coefficient to obtain a provisional output y[m].Then, the post-stage FIR coefficient computation unit 52 calculates them-th tap coefficient by a 2×2 matrix minimum mean square error method(MMSE) with the difference between the known symbol reference value andthe above provisional output y[m] as a target value. Specifically, thepost-stage FIR coefficient computation unit 52 extracts the m-th columncorresponding to the m-th tap coefficient from the above-describedX-polarized input matrix PST_xall to obtain PST_xall[:, m]. Similarlyfor the Y-polarization, the post-stage FIR coefficient computation unit52 extracts the m-th column corresponding to the m-th tap coefficientfrom the input matrix PST_yall to obtain PST_yall[:, m]. The post-stageFIR coefficient computation unit 52 couples the two column vectorsPST_xall[:, m] and PST_yall[:, m] in the horizontal direction to obtaina rectangular matrix having N_PST_AVG rows in the vertical direction andtwo columns in the horizontal direction. This matrix is referred to asan m-th XY-polarized input matrix. The post-stage FIR coefficientcomputation unit 52 performs matrix computation (multiplication) of thecomplex conjugate transposed matrix of the m-th XY-polarized inputmatrix and the m-th XY-polarized input matrix, and further divides theresult by N_PST_AVG to obtain a 2×2 covariance matrix.

Moreover, the post-stage FIR coefficient computation unit 52 computes acomplex conjugate transposed matrix of the m-th XY-polarized inputmatrix for the known symbol column vector ref to obtain a two-componentcolumn vector.

The post-stage FIR coefficient computation unit 52 computes the 2×2covariance matrix for the two-component column vector to obtain hxx[m]and hxy[m].

The post-stage FIR coefficient computation unit 52 performs the aboveoperation for each m satisfying 1 m N_PST, that is, repeats the aboveoperation for the number of taps N_PST while changing m, to obtain allthe filter coefficients of the post-stage 2×2 FIR filter 42. Note thatthe order in which the post-stage FIR coefficient computation unit 52selects m may be, for example, a method of starting from the center tapand sequentially selecting the peripheral taps outward.

The post-stage FIR coefficient computation unit 52 may further repeatthe operation of obtaining a coefficient for each above m satisfying 1 mN_PST a plurality of times. The post-stage FIR coefficient computationunit 52 can increase the accuracy of the estimation value by performingsuch repetition. In this case, specifically, the post-stage FIRcoefficient computation unit 52 can use the filter coefficients of N_PSTtime positions obtained at the i-th time (i≥1) as the (i+1)-th (next)initial value. Also in the i-th operation (i≥2), similarly to the firstoperation described above, the post-stage FIR coefficient computationunit 52 can repeat estimation of coefficients other than the filtercoefficient at the m-th time position by using the latest value obtainedat that time.

Moreover, the post-stage FIR coefficient computation unit 52 may select,for example, two tap time positions as the m, and perform similarcomputation for the selected two tap time positions in parallel. In thiscase, the post-stage FIR coefficient computation unit 52 selects, forexample, two time positions of m1 and m2 when obtaining a provisionaloutput value of the post-stage 2×2 FIR filter 42.

In the computation of obtaining the m1-th tap coefficient, thepost-stage FIR coefficient computation unit 52 uses the latest valueobtained at that time including hxx[m2] and hxy[m2] as coefficientsexcluding hxx[m1] and hxy[m1]. The post-stage FIR coefficientcomputation unit 52 computes a filter on the basis of such acoefficient, obtains a provisional output value y[m1], and obtains anerror from the known symbol. Furthermore, the post-stage FIR coefficientcomputation unit 52 obtains hxx[m1] and hxy[m1] by computation of atwo-dimensional minimum mean square error method (MMSE) using the m1-thXY-polarized input matrix, similarly to the above description.

At the same time as the above m1-th time, the post-stage FIR coefficientcomputation unit 52 uses the latest value obtained at that timeincluding hxx[m1] and hxy[m1] as coefficients excluding hxx[m2] andhxy[m2] in the computation for obtaining the m2-th tap coefficient. Thepost-stage FIR coefficient computation unit 52 performs computation of afilter on the basis of such a coefficient, obtains a provisional outputvalue y[m2], and obtains an error from the known symbol. Furthermore,the post-stage FIR coefficient computation unit 52 obtains hxx[m2] andhxy[m2] by computation of a two-dimensional minimum mean square errormethod (MMSE) using the m2-th XY-polarized input matrix, similarly tothe above description.

As described above, the post-stage FIR coefficient computation unit 52performs computation of obtaining the tap coefficients for a pluralityof time positions of the post-stage 2×2 FIR filter 42 in parallel, sothat there is an advantage that the time required to calculate thecoefficients can be reduced as a whole. Note that, although an exampleof obtaining the tap coefficients for two time positions (m1 and m2) inparallel has been described above, tap coefficients for three or moretime positions may be obtained in parallel.

Here, there is a problem that a coefficient computation error mayincrease because a phase rotation occurs for each symbol in a case wherethere is a frequency offset. In order to solve this problem, thepost-stage FIR coefficient computation unit 52 may multiply eachcomponent of the known symbol column vector by the complex conjugate ofthe frequency offset phase compensation vector foc_phi_vec. As a result,the error in the coefficient obtained by the post-stage FIR coefficientcomputation unit 52 can be reduced. Moreover, in a case where the phasenoise is large, the post-stage FIR coefficient computation unit 52 maysimilarly multiply each component of the known symbol column vector bythe complex conjugate of the CPR phase compensation amount vectorcpr_phi_vec. As a result, the error in the coefficient obtained by thepost-stage FIR coefficient computation unit 52 can be reduced.

The post-stage FIR coefficient computation unit 52 can obtain acoefficient close to the n-tap coefficient that is the computationresult of a multi-dimensional minimum mean square error method (MMSE) byrepeating the above computation a plurality of times. The filtercoefficients hyx and hyy for obtaining the Y-polarized output can alsobe obtained by a method similar to that for the X-polarized output.

The post-stage 2×2 FIR filter 42 obtains an X-polarized and Y-polarizedoutput using the filter coefficient obtained by the post-stage FIRcoefficient computation unit 52. The CPR phase estimation unit 61estimates the carrier phase compensation amount by comparing theobtained X-polarized output value and the Y-polarized output value withthe known symbol. By averaging the errors between the output value fromthe post-stage 2×2 FIR filter 42 and the known symbol over a pluralityof symbols by the CPR phase estimation unit 61, a stable CPR estimationvalue can be obtained even under a condition where noise is large.

Moreover, the frequency offset can also be estimated by detecting adifference between the preceding and following symbols of the carrierphase compensation amount, that is, by detecting the slope of thecarrier phase compensation amount. The coefficient computation unit 80compensates for the carrier phase of the output from the post-stage FIRcoefficient computation unit 52 using the obtained frequency offsetestimation value and carrier phase compensation amount, and restores thetransmission state.

The pre-stage FIR coefficient computation unit 51 updates the tapcoefficient of the pre-stage 2×2 FIR filter 41 using the error betweenthe signal on which the frequency offset compensation and the carrierphase compensation have been performed and the known symbol.Specifically, the pre-stage FIR coefficient computation unit 51subtracts the carrier-phase-compensated output signal from the knownsymbol reference value to obtain the error. The error for X-polarizationis denoted by e_x. The error for Y polarization is denoted by e_y. Eachof the errors e_x and e_y is a complex error.

In the computation for updating the filter coefficient of the pre-stage2×2 FIR filter 41, the input value to the pre-stage 2×2 FIR filter 41corresponding to the output symbol of the carrier phase compensationused to obtain the symbol, and the filter coefficient of the post-stage2×2 FIR filter 42 used to compute the symbol are also required. Inpractice, these values are held in a buffer, and the pre-stage FIRcoefficient computation unit 51 is configured to read the values fromthe buffer. This is because a processing delay occurs until the outputof the carrier phase compensation is obtained. Instead of holding theabove values in a buffer, a delay may be given in the circuit to holdthe value.

In order to obtain one output symbol of carrier phase compensation,N_PST samples are required as inputs to the post-stage 2×2 FIR filter42. A matrix in which continuous samples of input values to thepre-stage 2×2 FIR filter 41 used to obtain respective input values tothe post-stage 2×2 FIR filter 42 are arranged in the horizontaldirection as column vectors by the amount of the input samples to thepost-stage 2×2 FIR filter 42 is defined as a pre-stage 2×2 FIR filterinput matrix. Pre-stage 2×2 FIR filter input matrices respectively for Xpolarization and Y polarization are denoted by pre_in_x and pre_in_y.The size of each of the matrices pre_in_x and pre_in_y is N_PRE rows inthe vertical direction and N_PST columns in the horizontal direction.

The pre-stage FIR coefficient computation unit 51 can calculate anupdate vector of the coefficient of the pre-stage 2×2 FIR filter 41 bythe gradient method. In this calculation, the pre-stage FIR coefficientcomputation unit 51 uses the above pre-stage FIR filter input matricespre_in_x and pre_in_y respectively for X polarization and Ypolarization, the errors e_x and e_y obtained respectively by thecarrier phase compensation outputs for X polarization and Ypolarization, and phi_x and phi_y that are complex numberrepresentations of carrier phase compensation amounts respectively for Xpolarization and Y polarization.

The configuration of the pre-stage 2×2 FIR filter 41 is as follows. Thatis, the pre-stage 2×2 FIR filter 41 includes a portion having the sum ofthe X-polarized input multiplied by pre_hxx and the Y-polarized inputmultiplied by pre_hxy as the X-polarized output. Moreover, the pre-stage2×2 FIR filter 41 includes a portion having the sum of the X-polarizedinput multiplied by pre_hyx and the Y-polarized input multiplied bypre_hyy as the Y-polarized output.

The update vector of the coefficient pre_hxx of the pre-stage 2×2 FIRfilter 41 is calculated by the following formula.

e_x×conj(pre_in_x×hxx×phi_x)+e_y×conj(pre_in_x×hyx×phi_y);

The update vector of the coefficient pre_hxy of the pre-stage 2×2 FIRfilter 41 is calculated by the following formula.

e_x×conj(pre_in_y×hxx×phi_x)+e_y×conj(pre_in_y×hyx×phi_y);

The update vector of the coefficient pre_hyx of the pre-stage 2×2 FIRfilter 41 is calculated by the following formula.

e_x×conj(pre_in_x×hxy×phi_x)+e_y×conj(pre_in_x×hyy×phi_y);

The update vector of the coefficient pre_hyy of the pre-stage 2×2 FIRfilter 41 is calculated by the following formula.

e_x×conj(pre_in_y×hxy×phi_x)+e_y×conj(pre_in_y×hyy×phi_y);

In each of the above formulas, conj( ) means a complex conjugate. Thepre-stage FIR coefficient computation unit 51 updates each coefficientby multiplying each of the update vectors by a step size and adding theresult to the latest coefficient (pre_hxx, pre_hxy, pre_hyx, andpre_hyy, respectively).

In other words, the pre-stage FIR coefficient computation unit 51performs the following processing. The pre-stage FIR coefficientcomputation unit 51 performs frequency offset compensation and carrierphase compensation on the output of the post-stage 2×2 FIR filter 42.For the output of the frequency offset compensation and the carrierphase compensation, the pre-stage FIR coefficient computation unit 51computes a complex error from the known symbol corresponding to the timeposition. In order to obtain an output from the post-stage 2×2 FIRfilter 42 corresponding to a time position of a certain known signalsymbol, the pre-stage FIR coefficient computation unit 51 obtains aninner product of the coefficient of the pre-stage 2×2 FIR filter 42 andcontinuous (N−M+1) samples obtained by multiplication by the coefficientof the n-th pre-stage 2×2 FIR filter 41 in the convolution computationof the pre-stage 2×2 FIR filter 41, which are input samples to thepre-stage 2×2 FIR filter 41 used to obtain (N−M+1 samples) inputted tothe post-stage 2×2 FIR filter 42. Furthermore, the pre-stage FIRcoefficient computation unit 51 multiplies the inner product value by acomplex number representing the phase rotation for frequency offsetcompensation and a complex number representing the phase rotation forcarrier phase compensation, which are applied to the output from thepost-stage 2×2 FIR filter 42. The pre-stage FIR coefficient computationunit 51 obtains an update vector by multiplying the value obtained bycomputing a product of the complex conjugate and the complex error by astep size. The pre-stage FIR coefficient computation unit 51 adds theupdate vector to the coefficient of the n-th pre-stage 2×2 FIR filter 41and sets the result as the coefficient of the n-th pre-stage 2×2 FIRfilter 41.

[Convolution Computation]

By the processing process described above, the coefficient of thepre-stage 2×2 FIR filter 41 and the coefficient of the post-stage 2×2FIR filter 42 optimized using the known signal are individuallyobtained. The convolution computation unit 71 obtains the tapcoefficient of the main signal filter by the convolution computation ofthe optimized coefficients of the pre-stage FIR and the post-stage FIR.

Specifically, the convolution computation unit 71 obtains the tapcoefficient of X-polarized input—X-polarized output of the main signalfilter as the sum of the convolution sequence of the coefficient hxx ofthe post-stage 2×2 FIR filter 42 and the coefficient pre_hxx of thepre-stage 2×2 FIR filter 41 and the convolution sequence of thecoefficient hxy of the post-stage 2×2 FIR filter 42 and the coefficientpre_hyx of the pre-stage 2×2 FIR filter 41. That is, the tap coefficientof X-polarized input—X-polarized output of the main signal filter iscomputed as conv(hxx, pre_hxx)+conv(hxy, pre_hyx). Note that, con( )here represents convolution computation, and the same applies to thefollowing.

Moreover, the convolution computation unit 71 obtains the tapcoefficient of Y-polarized input—X-polarized output of the main signalfilter as the sum of the convolution sequence of the coefficient hxx ofthe post-stage 2×2 FIR filter 42 and the coefficient pre_hxy of thepre-stage 2×2 FIR filter 41 and the convolution sequence of thecoefficient hxy of the post-stage 2×2 FIR filter 42 and the coefficientpre_hyy of the pre-stage 2×2 FIR filter 41. That is, the tap coefficientof Y-polarized input—X-polarized output of the main signal filter iscomputed as conv(hxx, pre_hxy)+conv(hxy, pre_hyy).

Moreover, the convolution computation unit 71 obtains the tapcoefficient of X-polarized input—Y-polarized output of the main signalfilter as the sum of the convolution sequence of the coefficient hyx ofthe post-stage 2×2 FIR filter 42 and the coefficient pre_hxx of thepre-stage 2×2 FIR filter 41 and the convolution sequence of thecoefficient hyy of the post-stage 2×2 FIR filter 42 and the coefficientpre_hyx of the pre-stage 2×2 FIR filter 41. That is, the tap coefficientof X-polarized input—Y-polarized output of the main signal filter iscomputed as conv(hyx, pre_hxx)+conv(hyy, pre_hyx).

Moreover, the convolution computation unit 71 obtains the tapcoefficient of Y-polarized input—Y-polarized output of the main signalfilter as the sum of the convolution sequence of the coefficient hyx ofthe post-stage 2×2 FIR filter 42 and the coefficient pre_hxy of thepre-stage 2×2 FIR filter 41 and the convolution sequence of thecoefficient hyy of the post-stage 2×2 FIR filter 42 and the coefficientpre_hyy of the pre-stage 2×2 FIR filter 41. That is, the tap coefficientof Y-polarized input—Y-polarized output of the main signal filter iscomputed as conv(hyx, pre_hxy)+conv(hyy, pre_hyy).

In the main signal FIR filter (FIR filters 11, 12, 13, and 14), theadaptive equalization FIR filter 1 applies the tap coefficient ofX-polarized input—X-polarized output, the tap coefficient of Y-polarizedinput—X-polarized output, the tap coefficient of X-polarizedinput—Y-polarized output, and the tap coefficient of Y-polarizedinput—Y-polarized output obtained above. The adaptive equalization FIRfilter 1 further applies FOC/CPR phase compensation on the main signal,and outputs the main signal after carrier phase compensation.

The computation and control functions of the adaptive equalization FIRfilter 1 can be configured using a processor such as a centralprocessing unit (CPU) or a graphics processing unit (GPU) and a memory.The above GPU may be configured to perform so-called GPGPU(general-purpose computing on graphics processing units; general-purposecomputation by GPU). The processor executes the program to function asat least one of the FIR filters 11, 12, 13, and 14, the adders 31 and33, and the coefficient computation unit 80 (the pre-stage 2×2 FIRfilter 41, the post-stage 2×2 FIR filter 42, the pre-stage FIRcoefficient computation unit 51, the post-stage FIR coefficientcomputation unit 52, the CPR phase estimation unit 61, and theconvolution computation unit 71). Note that all or some of the functionsof the adaptive equalization FIR filter 1 may be implemented by usinghardware such as an application specific integrated circuit (ASIC), aprogrammable logic device (PLD), or a field programmable gate array(FPGA). The above program may be recorded on a computer-readablerecording medium. The computer-readable recording medium is, forexample, a portable medium such as a flexible disk, a magneto-opticaldisc, a ROM, a CD-ROM, or a semiconductor storage device (e.g., a solidstate drive (SSD)), or a storage device such as a hard disk or asemiconductor storage device built in a computer system. The“computer-readable recording medium” may be a non-transitorycomputer-readable recording medium. The above program may be transmittedvia an electric communication line.

The adaptive equalization FIR filter configured as described above has afeedforward following configuration circuit in addition to aconventional general adaptive equalization filter configuration, therebyachieving both a high dynamic following speed and a high distortioncompensation resistance.

VARIATIONS

In the embodiment described above, another filter (e.g., an IIR filter)may be used instead of the FIR filter. In the above embodiment, thepost-stage FIR coefficient computation unit 52 obtains the filtercoefficient of the post-stage 2×2 FIR filter 42 by feedforward controlusing the minimum mean square error method. However, the post-stage FIRcoefficient computation unit 52 may obtain the filter coefficient of thepost-stage 2×2 FIR filter 42 by feedforward control using another methodinstead of the minimum mean square error method so as to reduce theerror between the inputted symbol and the value of the known symbol.

Although an embodiment of the present invention has been described abovein detail with reference to the drawings, specific configurations arenot limited to the embodiment, and include designs and the like notdeparting from the spirit of the present invention.

INDUSTRIAL APPLICABILITY

The present invention is applicable to, for example, an opticaltransmission system. However, the use range of the present invention isnot limited to that exemplified herein.

REFERENCE SIGNS LIST

-   -   1 Adaptive equalization FIR filter    -   11, 12, 13, 14 FIR filter (main signal FIR filter)    -   31, 33 Adder    -   41 Pre-stage 2×2 FIR filter    -   42 Post-stage 2×2 FIR filter    -   51 Pre-stage FIR coefficient computation unit    -   52 Post-stage FIR coefficient computation unit    -   61 CPR phase estimation unit    -   71 Convolution computation unit    -   80 Coefficient computation unit

1. An adaptive equalization filter for an optical transmission system,comprising: a main signal filter; and a coefficient computation unitthat updates a filter coefficient of the main signal filter, wherein thecoefficient computation unit includes: a pre-stage filter and apost-stage filter that are connected in cascade, each having a sample ofa main signal as an input; a pre-stage coefficient computation unit thatobtains a filter coefficient of the pre-stage filter by feedback controlusing a gradient method; a post-stage coefficient computation unit thatobtains a filter coefficient of the post-stage filter by feedforwardcontrol; and a convolution computation unit that obtains a filtercoefficient of the main signal filter by convolution computation of afilter coefficient of the pre-stage filter obtained by the pre-stagecoefficient computation unit and a filter coefficient of the post-stagefilter obtained by the post-stage coefficient computation unit.
 2. Theadaptive equalization filter according to claim 1, wherein thepost-stage coefficient computation unit obtains an inverse matrix of acovariance matrix of an input signal vector to the post-stage filter,and obtains a correlation vector between a known signal symbol and aninput signal vector to the post-stage filter by using a plurality ofsets of an input signal vector to the post-stage filter and a knownsignal symbol at a time position obtained by applying the post-stagefilter to the input signal vector, and applies an inverse matrix of thecovariance matrix to the correlation vector to obtain a filtercoefficient of the post-stage filter using a minimum mean square errormethod.
 3. The adaptive equalization filter according to claim 1,wherein the post-stage filter is a filter having two inputs and twooutputs, and the post-stage coefficient computation unit obtains afilter coefficient of the post-stage filter, with one of coefficients oflength M taps of two inputs of the post-stage filter denoted by hx[1],hx[2], . . . , and hx[M], and the other of the coefficients denoted byhy[1], hy[2], . . . , and hy[M], by selecting one or a plurality of taptime positions m from the M taps and performing, for each selected m,the steps of: applying a filter coefficient at a tap time position otherthan the tap time position m to an input signal vector to the pre-stagefilter to compute a provisional value y[m] of an output symbol of thepost-stage FIR filter; calculating a complex error between a complexvalue of a known signal symbol corresponding to a time position of theprovisional value y[m] and a complex value of the provisional valuey[m]; using one or a plurality of sets of the complex error and an inputsignal vector to the post-stage filter used to compute the provisionalvalue y[m] to obtain an inverse matrix of a 2×2 covariance matrix of aninput signal vector to the post-stage filter and obtain a correlationvector between the complex error and an input signal vector to thepost-stage filter; and applying an inverse matrix of the 2×2 covariancematrix to the correlation vector to calculate hx[m] and hy[m] as a m-thtap coefficient.
 4. The adaptive equalization filter according to claim2, wherein the post-stage coefficient computation unit performscomputation of multiplying each of the known signal symbols by a complexconjugate of a phase rotation amount predicted from an estimatedfrequency offset amount.
 5. The adaptive equalization filter accordingto claim 4, wherein the post-stage coefficient computation unit furtherperforms computation, for each of the known signal symbols, ofmultiplication by a complex conjugate of the carrier phase compensationamount for a symbol for which a carrier phase compensation amount hasalready been estimated, and multiplication by a complex conjugate of arepresentative value of a phase compensation amount of a symbol forwhich a carrier phase compensation amount has already been estimated fora symbol for which a carrier phase compensation amount has not beenestimated yet.
 6. The adaptive equalization filter according to claim 1,wherein the pre-stage coefficient computation unit obtains a filtercoefficient of the pre-stage filter using a gradient method in a mannersuch that an error between an output signal from the post-stage filterand a known signal decreases.
 7. The adaptive equalization filteraccording to claim 1, wherein the pre-stage coefficient computation unitcomputes and updates a filter coefficient of the pre-stage filter by:computing a complex error between a result of performing frequencyoffset compensation and carrier phase compensation on an output signalfrom the post-stage filter and a known symbol at a same time position;calculating an inner product of an input sample to the pre-stage filterused to obtain an output signal from the post-stage filter and acoefficient of the post-stage filter, further applying the frequencyoffset compensation and the carrier phase compensation, and obtaining anupdate vector on a basis of a product of a complex conjugate of anapplication result and the complex error; and multiplying the updatevector by a step size.
 8. A filter coefficient update method forupdating a filter coefficient of a main signal filter, wherein apre-stage filter and a post-stage filter are connected in cascade with asample of a main signal as an input, a pre-stage coefficient computationunit obtains a filter coefficient of the pre-stage filter by feedbackcontrol using a gradient method, a post-stage coefficient computationunit obtains a filter coefficient of the post-stage filter byfeedforward control, and a convolution computation unit obtains a filtercoefficient of the main signal filter by convolution computation of afilter coefficient of the pre-stage filter obtained by the pre-stagecoefficient computation unit and a filter coefficient of the post-stagefilter obtained by the post-stage coefficient computation unit.